Collision of solitons in neuronal microtubules with dipole–dipole interaction

In this paper, we investigate the collision dynamics of solitons in neuronal microtubules. We have used a continuum equation of the type nonlinear Schrödinger equation with the presence of dipole–dipole interaction and electric field. The continuous nonlinear Schrödinger equation serves as an effective framework for describing soliton solutions and we have developed one and two soliton solutions using the Hirota bilinear method. We examine the behaviour of solitons in neuronal microtubules and extend our analysis to the collision dynamics of two solitons under varying dipole–dipole interactions. Our results show an intricate interplay between the collision dynamics of solitons and the effect of dipole–dipole interaction in neuronal microtubules. Further, the stability of the soliton solution is discussed with the help of the Fourier collocation method. This work is important for understanding the complex interaction between solitons and also provides crucial insights into microtubule properties. The effect of dipole–dipole interactions on these collisions may play a significant role in the propagation of coherent quantum states in the brain. • Collision dynamics of solitons in neuronal microtubules is studied. • The dynamical model is solved using Hirota bilinearization method and obtained one and two soliton solution. • Observed dynamics of the inelastic collision of solitons in neuronal microtubules. • The effect of dipole–dipole interaction on the collision dynamics of solitons is observed.